^2 log 1/4 akar 8 = ..... ??? caranya yaa.... Question from @erlandryfakhri

October 2018 2 70 Report

^2 log 1/4 akar 8 = ..... ???

caranya yaa

whongaliem $^{2}log$ $\frac{1}{4} \sqrt{8}$ = $^{2}log$ $\frac{1}{4}$ + $^{2}log \sqrt{8}$
= $^{2}log 2^{- 2}$ + $^{2}log 8^{ \frac{1}{2} }$
= - 2 . $^{2}log 2$ + $^{2}log (2^{3}) ^{ \frac{1}{2} }$
= - 2 . 1 + $^{2}log 2^{ \frac{3}{2} }$
= - 2 + $\frac{3}{2}$ . $^{2}log 2$
= - 2 + $\frac{3}{2}$ . 1
= - 2 + $\frac{3}{2}$
= $-\frac{1}{2}$

1 votes Thanks 2

Takamori37 $$\begin{align}^2\log\frac14\sqrt8&=\,^2\log\left[\frac1{2^2}\times\sqrt{2^3}\right] \\ &=\,^2\log\left[2^{-2}\times2^{\textstyle\frac32}\right] \\ &=\,^2\log(2^{-2+\!\!\textstyle\frac32})&&||\text{ Operasi perpangkatan} \\ &=\,^2\log 2^{-\textstyle\frac12} \\ &=-\frac12\times\,^2\log 2&&||\text{ Sifat pangkat numerus} \\ &=-\frac12\times1 \\ &=-\frac12\end{align}$

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